Fractional optimal control problems: a pseudo-state-space approach

Abstract

A scheme for optimal control problem formulation and solution of a fractional order system using pseudo-state-space formulation is presented in this paper. A pseudo-state-space representation for a particular type of fractional dynamical equation is proposed. The dynamic constraint is in the form of a fractional differential equation that includes integer derivatives in addition to the fractional derivatives. The order of the fractional derivatives is taken as less than one and fractional derivatives are defined in terms of Riemann-Liouville. The performance index considered is a function of both the state and the control variables. Using the proposed pseudo-state-space model a new formulation of a class of fractional optimal control problem is developed. A direct numerical technique based on Grunwald-Letnikov approximation is used to solve the resulting equations. A numerical example of a fractional order spring-mass-viscodamper system is considered to illustrate the methodology and technique.